To calculate the work (W) required to expand the volume of the pump against an external pressure, we can use the formula:
\[ W = -P_{\text{ext}} \times \Delta V \]
Where:
\( W \) = Work (in Joules, J)
\( P_{\text{ext}} \) = External pressure (in atm)
\( \Delta V \) = Change in volume (in liters)
Given:
Initial volume (\( V_{\text{initial}} \)) = 0.0 L
Final volume (\( V_{\text{final}} \)) = 2.7 L
External pressure (\( P_{\text{ext}} \)) = 1.2 atm
Now, calculate the change in volume (\( \Delta V \)):
\[ \Delta V = V_{\text{final}} - V_{\text{initial}} \]
\[ \Delta V = 2.7 L - 0.0 L \]
\[ \Delta V = 2.7 L \]
Next, calculate the work (W):
\[ W = -P_{\text{ext}} \times \Delta V \]
\[ W = -(1.2 \, \text{atm}) \times (2.7 \, \text{L}) \]
Now, we need to convert atm⋅L to Joules since 1 atm⋅L = 101.325 J:
\[ W = -(1.2 \, \text{atm}) \times (2.7 \, \text{L}) \times (101.325 \, \text{J}) \]
Finally, calculate the value of W (rounding to two significant figures):
\[ W \approx -328 \, \text{J} \]
The work required to expand the volume of the pump from 0.0 L to 2.7 L against an external pressure of 1.2 atm is approximately -328 J (note that the negative sign indicates work done against the external pressure).